function J = jacobian(x, mu, k)
    % 计算 MCLM 模型的 Jacobian 矩阵
    % state: [X, Y, Z]
    
    X = x(1);
    Y = x(2);
    Z = x(3);
    
    % 根据论文（公式7）计算雅可比矩阵
    J = zeros(3,3);
    J(1,1) = mu - 2*mu*X + k*sin(Z);
    J(1,2) = -k*sin(Z);
    J(1,3) = k*(X - Y)*cos(Z);
    
    J(2,1) = -k*sin(Z);
    J(2,2) = mu - 2*mu*Y + k*sin(Z);
    J(2,3) = -k*(X - Y)*cos(Z);
    
    J(3,1) = 1;
    J(3,2) = -1;
    J(3,3) = 1;
end
